Question

The diagram shows 3 vertices of a parallelogram.
Plot the 3 possible points for the 4th vertex.

Answer 1

Answer:

(-1, -1), (-3,5), (5, -3)

Step-by-step explanation:

Answer 2

(-1, -1) is the 4th vertex.

Which is the required vertex ?

Let, 4th vertex is (x, y)

Given vertices of parallelogram are (-2. 2), (1, 1), (2, -2)

Here, (-2. 2) & (2, -2) are opposite vertices.

So, Midpoint of diagonals = $[(\frac{-2+2}{2}) ,(\frac{2-2}{2})]$ = (0, 0)

This is also midpoint of diagonal with vertices (1, 1) & (x, y)

So, (1+x)/2=0 ⇒ x = -1

& (1+y)/2=0 ⇒ y = -1

∴ 4th vertex is (-1, -1)

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